<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we consider the partition function <italic>Q</italic>(<italic>n</italic>) counting the partitions of <italic>n</italic> into distinct parts and investigate congruence identities of the form
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2022-0040_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>Q</mi><mrow><mo>(</mo><mrow><mi>p</mi><mo>⋅</mo><mi>n</mi><mo>+</mo><mfrac><mrow><msup><mrow><mi>p</mi></mrow><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow><mrow><mn>24</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mo>≡</mo><mn>0</mn><mi> </mi><mi> </mi><mi> </mi><mrow><mo>(</mo><mrow><mo>mod</mo><mn>4</mn></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math>
<tex-math>Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left( {\bmod 4} \right),</tex-math>
</alternatives>
</disp-formula>
where <italic>p</italic> ⩾ 5 is a prime.</p>
</abstract>

In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the form



Q(p⋅n+p2-124)≡0   (mod4),
Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left( {\bmod 4} \right),


where p ⩾ 5 is a prime.

Ramanujan-type congruences modulo 4 for partitions into distinct parts

Department of Mathematical Methods and Models

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Ramanujan-type congruences modulo 4 for partitions into distinct parts"}

In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the...

Ramanujan-type congruences modulo 4 for partitions into distinct parts

Published Online: Oct 08, 2022

Page range: 185 - 199

Received: Dec 04, 2021

Accepted: Apr 15, 2022

DOI: https://doi.org/10.2478/auom-2022-0040

Keywords
Partitions, Congruences, Divisors

© 2022 Mircea Merca, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Ramanujan-type congruences modulo 4 for partitions into distinct parts

Published Online: Oct 08, 2022

Page range: 185 - 199

Received: Dec 04, 2021

Accepted: Apr 15, 2022

DOI: https://doi.org/10.2478/auom-2022-0040

KeywordsPartitions, Congruences, Divisors

© 2022 Mircea Merca, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Partitions, Congruences, Divisors